# An analytical study describing one approach to company modeling

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## Abstract

Prior to World War II most problems in the field of business were solved either subjectively or intuitively. Those problems which could be solved analytically were of such a nature that it required, at most, an adding machine to solve them. However, beginning with and following World War II, important developments in the fields of mathematics and electronics have made it possible to expand greatly the range of business problems that can now be solved analytically. Those in the areas of industrial engineering and economics have made substantial use of these new developments, which is in contrast to the area of business. There are varied reasons for thus, one being the lack of meaningful information. The purpose of this thesis is to develop an approach by which more comprehensive mathematical models of operations can be constructed for a company which will enable it to better obtain more meaningful information concerning business problems which previously could only be solved subjectively. This will be done in such a manner that, if necessary, the mathematical model may be changed and improved with a minimum of effort. While a mathematical model is developed in this thesis, this is merely done as an example of an approach to how other mathematical models can be developed. The model used in this thesis is limited to the major operations found in an average company ad does not consider the operations of the economy as a whole or in part. No effort is made to develop the mathematical theory used in the linear programming models. There is nothing special about certain of the sub-models being linear programming models, they may well have been non-linear or various other mathematical types. It is beyond the scope of this thesis to explain the mathematics of these various models as they are both very detailed and commonly found in current texts today. Basically, an engineering approach will b used in developing the operation al model. The company will be broken down by major departments and a sub-model constructed for each. Then financial information from each sub-model will be used for a central input-output financial matrix. From this central financial matrix an overall picture of the operations of the company as a whole can be seen as well as the interrelations between departments. This approach has the advantage of flexibility. If, for example, a newer and better production model is developed, it can be used without incurring any major revisions. Another approach (a mathematical one) would be to develop a single mathematical matrix which defines the operations of a company. In such a case, if a newer and better production model is developed it may well require a major revision of the mathematical matrix. An engineering approach avoids this. Three types of business problems have been discussed in Chapter II; subjective problems, analytic problems, and intuitive problems. It is the analytic solution of certain problems which previously could only be solved intuitively with which this thesis is concerned. An analogous breakdown model of a common radio is compared with a breakdown model of a company. A simple example of a financial input-output matrix is examined for a company and various relationships derived from it. One of the more important definition was that of net profit where [mathematical equation pictured]. The overall company model presented in Chapter III consisted of a financial model, a production model, a labor model, and a transportation model. While these different models are developed separately, they are shown to be interdependent. The basis of the financial model, Matrix A, is a matrix which defines the flow of money from various sections having a financial contribution to various departments having financial necessity. The production model, Matrix B, is a linear programming model which minimizes the total daily production cost. The labor model, Matrix C, is a linear programming model which minimizes the total cost of labor for each factory. The transportation model, Matrix D, is a transportation model which determines the minimum total cost of transportation for all products produced by the company and shipped to buyers.